Question

, evaluate and simplify.

Answer 1

`f(x)=4x^2-5x \\\\[-0.35em] ~\dotfill\\\\ \cfrac{f(x+h)~~ - ~~f(x)}{h}\implies \cfrac{[4(x+h)^2 - 5(x+h)]~~ - ~~[4x^2-5x]}{h} \\\\\\ \cfrac{[4(x^2+2hx+h^2) - 5(x+h)]~~ - ~~[4x^2-5x]}{h} \\\\\\ \cfrac{4x^2+8hx+4h^2-5x-5h~~ - ~~4x^2+5x}{h}\implies \cfrac{8hx+4h^2-5h}{h} \\\\\\ \cfrac{h(8x+4h-5)}{h}\implies 8x+4h-5`